In [1]:
import sys
#!{sys.executable} -m pip install 
#!conda install --yes --prefix {sys.prefix} 
sys.path.append('../')
from ISI import Problem, Solution, excel_to_pb, Meta_param, Matheuristic
import numpy as np
from copy import deepcopy

Building problems

In [2]:
path = '../Data/Burundi final v2.xlsx'
schools, warehouses, Q1, V_number, makes = excel_to_pb(path)
problem_global = Problem(warehouses, schools, Q1, V_number=V_number, makes=makes, T=2, H=1, time_step=0.5)
problem_global.time_fuse()
In [3]:
problems = problem_global.clustering()

Found 3 clusters!
In [4]:
problemBUJUMBURA,problemNGOZI,problemGITEGA = problems[0], problems[1], problems[2]
In [5]:
param = Meta_param(seed = 1)

Cluster of NGOZI

In [6]:
problem = problemNGOZI

Default parameters

In [7]:
problem1 = problem.copy()
problem1
Out[7]:
Parameters of the problem : 
         Number of time steps : 4 
         Number of schools : 50 
         Number of warehouses : 2 
          Name of the warehouses : ['BUJUMBURA', 'NGOZI'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 9 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 4 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 2 
         Number of virtual time steps between segments : 0.5 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0.5
In [8]:
param
Out[8]:
 Meta parameters of the heurestics : 
 
 For iterations : 
     Length of segments (delta) : 10 , 
     Tau (the temperature) begins at 3.0, finishes at 0.1 and is cooled by 0.9 --> 32 steps 
  
 Inside algorithm's parameters : 
     Bounds of epsilon  : (0.05, 0.15) , 
     For randomizing G (ksi) : 0.142 
 
     Operators' parameters : 
     Sigmas for updating the weigths of the operators (10, 5, 2), with reaction factor : 0.8 , 
     Percentage rho for operators : 0.3 , 
     Solver used for the MIP : CBC
In [9]:
heuristic1 = Matheuristic(problem1,param)
heuristic1.algo2()

 Total algorithm time = 744.05 
Total ISI running times : 
  Define problem  :  149.16
  Solve problem   :  580.72
  Compute TSPs  :  4.45
  Visualisation  :  0.19
In [10]:
heuristic1.plot_steps()
In [11]:
heuristic1.solution_best
Out[11]:
Solution with a total cost of 31.919  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  1.7326

With double number of vehicules

In [12]:
problem2 = problem.copy()
problem2.augment_v(2)
problem2
Out[12]:
Parameters of the problem : 
         Number of time steps : 4 
         Number of schools : 50 
         Number of warehouses : 2 
          Name of the warehouses : ['BUJUMBURA', 'NGOZI'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 18 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 4 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 2 
         Number of virtual time steps between segments : 0.5 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0.5
In [13]:
param
Out[13]:
 Meta parameters of the heurestics : 
 
 For iterations : 
     Length of segments (delta) : 10 , 
     Tau (the temperature) begins at 3.0, finishes at 0.1 and is cooled by 0.9 --> 32 steps 
  
 Inside algorithm's parameters : 
     Bounds of epsilon  : (0.05, 0.15) , 
     For randomizing G (ksi) : 0.142 
 
     Operators' parameters : 
     Sigmas for updating the weigths of the operators (10, 5, 2), with reaction factor : 0.8 , 
     Percentage rho for operators : 0.3 , 
     Solver used for the MIP : CBC
In [14]:
heuristic2 = Matheuristic(problem2,param)
heuristic2.algo2()

 Total algorithm time = 650.31 
Total ISI running times : 
  Define problem  :  408.56
  Solve problem   :  211.05
  Compute TSPs  :  4.56
  Visualisation  :  0.23
In [15]:
heuristic2.plot_steps()
In [16]:
heuristic2.solution_best
Out[16]:
Solution with a total cost of 32.867  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  1.7841

Without time splitting

In [17]:
problem3 = problem.copy()
problem3.H = 2
problem3
Out[17]:
Parameters of the problem : 
         Number of time steps : 4 
         Number of schools : 50 
         Number of warehouses : 2 
          Name of the warehouses : ['BUJUMBURA', 'NGOZI'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 9 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 4 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 2 
         Number of virtual time steps between segments : 0.5 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0.5
In [18]:
param
Out[18]:
 Meta parameters of the heurestics : 
 
 For iterations : 
     Length of segments (delta) : 10 , 
     Tau (the temperature) begins at 3.0, finishes at 0.1 and is cooled by 0.9 --> 32 steps 
  
 Inside algorithm's parameters : 
     Bounds of epsilon  : (0.05, 0.15) , 
     For randomizing G (ksi) : 0.142 
 
     Operators' parameters : 
     Sigmas for updating the weigths of the operators (10, 5, 2), with reaction factor : 0.8 , 
     Percentage rho for operators : 0.3 , 
     Solver used for the MIP : CBC
In [19]:
heuristic3 = Matheuristic(problem3,param)
heuristic3.algo2()

 Total algorithm time = 339.36 
Total ISI running times : 
  Define problem  :  159.22
  Solve problem   :  164.09
  Compute TSPs  :  4.67
  Visualisation  :  0.21
In [20]:
heuristic3.plot_steps()
In [21]:
heuristic3.solution_best
Out[21]:
Solution with a total cost of 36.604  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  1.7563

Without virtual time step

In [22]:
problem4 = problem.copy()
problem4.t_virt = 0
problem4.time_fuse(1/problem.t_virt)
problem4
Out[22]:
Parameters of the problem : 
         Number of time steps : 2 
         Number of schools : 50 
         Number of warehouses : 2 
          Name of the warehouses : ['BUJUMBURA', 'NGOZI'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 9 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 2 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 1 
         Number of virtual time steps between segments : 0 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0
In [23]:
param
Out[23]:
 Meta parameters of the heurestics : 
 
 For iterations : 
     Length of segments (delta) : 10 , 
     Tau (the temperature) begins at 3.0, finishes at 0.1 and is cooled by 0.9 --> 32 steps 
  
 Inside algorithm's parameters : 
     Bounds of epsilon  : (0.05, 0.15) , 
     For randomizing G (ksi) : 0.142 
 
     Operators' parameters : 
     Sigmas for updating the weigths of the operators (10, 5, 2), with reaction factor : 0.8 , 
     Percentage rho for operators : 0.3 , 
     Solver used for the MIP : CBC
In [24]:
heuristic4 = Matheuristic(problem4,param)
heuristic4.algo2()

 Total algorithm time = 91.13 
Total ISI running times : 
  Define problem  :  37.71
  Solve problem   :  44.72
  Compute TSPs  :  5.67
  Visualisation  :  0.13
In [25]:
heuristic4.plot_steps()
In [26]:
heuristic4.solution_best
Out[26]:
Solution with a total cost of 34.655  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  2.1923

With higher rho

In [27]:
problem5 = problem.copy()
problem5
Out[27]:
Parameters of the problem : 
         Number of time steps : 4 
         Number of schools : 50 
         Number of warehouses : 2 
          Name of the warehouses : ['BUJUMBURA', 'NGOZI'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 9 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 4 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 2 
         Number of virtual time steps between segments : 0.5 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0.5
In [28]:
param5 = deepcopy(param)
param5.rho_percent = 0.6
In [29]:
heuristic5 = Matheuristic(problem5,param5)
heuristic5.algo2()

 Total algorithm time = 340.71 
Total ISI running times : 
  Define problem  :  161.11
  Solve problem   :  163.79
  Compute TSPs  :  4.91
  Visualisation  :  0.24
In [30]:
heuristic5.plot_steps()
In [31]:
heuristic5.solution_best
Out[31]:
Solution with a total cost of 31.769  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  2.1426

With lower rho

In [32]:
problem6 = problem.copy()
problem6
Out[32]:
Parameters of the problem : 
         Number of time steps : 4 
         Number of schools : 50 
         Number of warehouses : 2 
          Name of the warehouses : ['BUJUMBURA', 'NGOZI'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 9 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 4 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 2 
         Number of virtual time steps between segments : 0.5 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0.5
In [33]:
param6 = deepcopy(param)
param6.rho_percent = 0.1
In [34]:
heuristic6 = Matheuristic(problem6,param6)
heuristic6.algo2()

 Total algorithm time = 257.71 
Total ISI running times : 
  Define problem  :  135.36
  Solve problem   :  110.14
  Compute TSPs  :  3.59
  Visualisation  :  0.18
In [35]:
heuristic6.plot_steps()
In [36]:
heuristic6.solution_best
Out[36]:
Solution with a total cost of 35.839  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  2.076

Cluster of GITEGA

In [37]:
problem = problemGITEGA

Default parameters

In [38]:
problem1 = problem.copy()
problem1
Out[38]:
Parameters of the problem : 
         Number of time steps : 4 
         Number of schools : 50 
         Number of warehouses : 2 
          Name of the warehouses : ['BUJUMBURA', 'GITEGA'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 8 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 4 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 2 
         Number of virtual time steps between segments : 0.5 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0.5
In [39]:
param
Out[39]:
 Meta parameters of the heurestics : 
 
 For iterations : 
     Length of segments (delta) : 10 , 
     Tau (the temperature) begins at 3.0, finishes at 0.1 and is cooled by 0.9 --> 32 steps 
  
 Inside algorithm's parameters : 
     Bounds of epsilon  : (0.05, 0.15) , 
     For randomizing G (ksi) : 0.142 
 
     Operators' parameters : 
     Sigmas for updating the weigths of the operators (10, 5, 2), with reaction factor : 0.8 , 
     Percentage rho for operators : 0.3 , 
     Solver used for the MIP : CBC
In [40]:
heuristic1 = Matheuristic(problem1,param)
heuristic1.algo2()

 Total algorithm time = 268.04 
Total ISI running times : 
  Define problem  :  153.87
  Solve problem   :  100.72
  Compute TSPs  :  4.89
  Visualisation  :  0.2
In [41]:
heuristic1.plot_steps()
In [42]:
heuristic1.solution_best
Out[42]:
Solution with a total cost of 32.517  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  1.9871

With double number of vehicules

In [43]:
problem2 = problem.copy()
problem2.augment_v(2)
problem2
Out[43]:
Parameters of the problem : 
         Number of time steps : 4 
         Number of schools : 50 
         Number of warehouses : 2 
          Name of the warehouses : ['BUJUMBURA', 'GITEGA'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 16 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 4 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 2 
         Number of virtual time steps between segments : 0.5 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0.5
In [44]:
param
Out[44]:
 Meta parameters of the heurestics : 
 
 For iterations : 
     Length of segments (delta) : 10 , 
     Tau (the temperature) begins at 3.0, finishes at 0.1 and is cooled by 0.9 --> 32 steps 
  
 Inside algorithm's parameters : 
     Bounds of epsilon  : (0.05, 0.15) , 
     For randomizing G (ksi) : 0.142 
 
     Operators' parameters : 
     Sigmas for updating the weigths of the operators (10, 5, 2), with reaction factor : 0.8 , 
     Percentage rho for operators : 0.3 , 
     Solver used for the MIP : CBC
In [45]:
heuristic2 = Matheuristic(problem2,param)
heuristic2.algo2()

 Total algorithm time = 664.29 
Total ISI running times : 
  Define problem  :  430.5
  Solve problem   :  203.33
  Compute TSPs  :  5.94
  Visualisation  :  0.28
In [46]:
heuristic2.plot_steps()
In [47]:
heuristic2.solution_best
Out[47]:
Solution with a total cost of 33.768  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  1.9362

Without time splitting

In [48]:
problem3 = problem.copy()
problem3.H = 2
problem3
Out[48]:
Parameters of the problem : 
         Number of time steps : 4 
         Number of schools : 50 
         Number of warehouses : 2 
          Name of the warehouses : ['BUJUMBURA', 'GITEGA'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 8 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 4 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 2 
         Number of virtual time steps between segments : 0.5 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0.5
In [49]:
param
Out[49]:
 Meta parameters of the heurestics : 
 
 For iterations : 
     Length of segments (delta) : 10 , 
     Tau (the temperature) begins at 3.0, finishes at 0.1 and is cooled by 0.9 --> 32 steps 
  
 Inside algorithm's parameters : 
     Bounds of epsilon  : (0.05, 0.15) , 
     For randomizing G (ksi) : 0.142 
 
     Operators' parameters : 
     Sigmas for updating the weigths of the operators (10, 5, 2), with reaction factor : 0.8 , 
     Percentage rho for operators : 0.3 , 
     Solver used for the MIP : CBC
In [50]:
heuristic3 = Matheuristic(problem3,param)
heuristic3.algo2()

 Total algorithm time = 214.4 
Total ISI running times : 
  Define problem  :  117.48
  Solve problem   :  85.2
  Compute TSPs  :  4.36
  Visualisation  :  0.17
In [51]:
heuristic3.plot_steps()
In [52]:
heuristic3.solution_best
Out[52]:
Solution with a total cost of 32.808  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  2.922

Without virtual time step

In [53]:
problem4 = problem.copy()
problem4.t_virt = 0
problem4.time_fuse(1/problem.t_virt)
problem4
Out[53]:
Parameters of the problem : 
         Number of time steps : 2 
         Number of schools : 50 
         Number of warehouses : 2 
          Name of the warehouses : ['BUJUMBURA', 'GITEGA'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 8 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 2 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 1 
         Number of virtual time steps between segments : 0 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0
In [54]:
param
Out[54]:
 Meta parameters of the heurestics : 
 
 For iterations : 
     Length of segments (delta) : 10 , 
     Tau (the temperature) begins at 3.0, finishes at 0.1 and is cooled by 0.9 --> 32 steps 
  
 Inside algorithm's parameters : 
     Bounds of epsilon  : (0.05, 0.15) , 
     For randomizing G (ksi) : 0.142 
 
     Operators' parameters : 
     Sigmas for updating the weigths of the operators (10, 5, 2), with reaction factor : 0.8 , 
     Percentage rho for operators : 0.3 , 
     Solver used for the MIP : CBC
In [55]:
heuristic4 = Matheuristic(problem4,param)
heuristic4.algo2()

 Total algorithm time = 105.76 
Total ISI running times : 
  Define problem  :  35.45
  Solve problem   :  60.33
  Compute TSPs  :  6.53
  Visualisation  :  0.15
In [56]:
heuristic4.plot_steps()
In [57]:
heuristic4.solution_best
Out[57]:
Solution with a total cost of 40.805  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  2.8161

With higher rho

In [58]:
problem5 = problem.copy()
problem5
Out[58]:
Parameters of the problem : 
         Number of time steps : 4 
         Number of schools : 50 
         Number of warehouses : 2 
          Name of the warehouses : ['BUJUMBURA', 'GITEGA'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 8 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 4 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 2 
         Number of virtual time steps between segments : 0.5 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0.5
In [59]:
param5 = deepcopy(param)
param5.rho_percent = 0.6
In [60]:
heuristic5 = Matheuristic(problem5,param5)
heuristic5.algo2()

Duration constraint looks infeasible
Duration constraint looks infeasible
Duration constraint looks infeasible
Duration constraint looks infeasible
Duration constraint looks infeasible
 Total algorithm time = 249.7 
Total ISI running times : 
  Define problem  :  135.11
  Solve problem   :  100.37
  Compute TSPs  :  5.91
  Visualisation  :  0.21
In [61]:
heuristic5.plot_steps()
In [62]:
heuristic5.solution_best
Out[62]:
Solution with a total cost of 29.137  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  2.1999

With lower rho

In [63]:
problem6 = problem.copy()
problem6
Out[63]:
Parameters of the problem : 
         Number of time steps : 4 
         Number of schools : 50 
         Number of warehouses : 2 
          Name of the warehouses : ['BUJUMBURA', 'GITEGA'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 8 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 4 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 2 
         Number of virtual time steps between segments : 0.5 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0.5
In [64]:
param6 = deepcopy(param)
param6.rho_percent = 0.1
In [65]:
heuristic6 = Matheuristic(problem6,param6)
heuristic6.algo2()

Duration constraint looks infeasible
 Total algorithm time = 229.54 
Total ISI running times : 
  Define problem  :  131.77
  Solve problem   :  83.9
  Compute TSPs  :  5.63
  Visualisation  :  0.2
In [66]:
heuristic6.plot_steps()
In [67]:
heuristic6.solution_best
Out[67]:
Solution with a total cost of 59.334  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  2.8069

Cluster of BUJUMBURA

In [69]:
problem = problemBUJUMBURA

Default parameters

In [70]:
problem1 = problem.copy()
problem1
Out[70]:
Parameters of the problem : 
         Number of time steps : 4 
         Number of schools : 107 
         Number of warehouses : 1 
          Name of the warehouses : ['BUJUMBURA'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 10 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 4 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 2 
         Number of virtual time steps between segments : 0.5 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0.5
In [71]:
param
Out[71]:
 Meta parameters of the heurestics : 
 
 For iterations : 
     Length of segments (delta) : 10 , 
     Tau (the temperature) begins at 3.0, finishes at 0.1 and is cooled by 0.9 --> 32 steps 
  
 Inside algorithm's parameters : 
     Bounds of epsilon  : (0.05, 0.15) , 
     For randomizing G (ksi) : 0.142 
 
     Operators' parameters : 
     Sigmas for updating the weigths of the operators (10, 5, 2), with reaction factor : 0.8 , 
     Percentage rho for operators : 0.3 , 
     Solver used for the MIP : CBC
In [72]:
heuristic1 = Matheuristic(problem1,param)
heuristic1.algo2()

Duration constraint looks infeasible
Duration constraint looks infeasible
Duration constraint looks infeasible
Duration constraint looks infeasible
 Total algorithm time = 1665.99 
Total ISI running times : 
  Define problem  :  665.66
  Solve problem   :  903.16
  Compute TSPs  :  22.13
  Visualisation  :  0.36
In [73]:
heuristic1.plot_steps()
In [74]:
heuristic1.solution_best
Out[74]:
Solution with a total cost of 66.038  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  7.3501

With double number of vehicules

In [75]:
problem2 = problem.copy()
problem2.augment_v(2)
problem2
Out[75]:
Parameters of the problem : 
         Number of time steps : 4 
         Number of schools : 107 
         Number of warehouses : 1 
          Name of the warehouses : ['BUJUMBURA'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 20 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 4 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 2 
         Number of virtual time steps between segments : 0.5 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0.5
In [76]:
param
Out[76]:
 Meta parameters of the heurestics : 
 
 For iterations : 
     Length of segments (delta) : 10 , 
     Tau (the temperature) begins at 3.0, finishes at 0.1 and is cooled by 0.9 --> 32 steps 
  
 Inside algorithm's parameters : 
     Bounds of epsilon  : (0.05, 0.15) , 
     For randomizing G (ksi) : 0.142 
 
     Operators' parameters : 
     Sigmas for updating the weigths of the operators (10, 5, 2), with reaction factor : 0.8 , 
     Percentage rho for operators : 0.3 , 
     Solver used for the MIP : CBC
In [77]:
heuristic2 = Matheuristic(problem2,param)
heuristic2.algo2()

 Total algorithm time = 2777.42 
Total ISI running times : 
  Define problem  :  1408.37
  Solve problem   :  1175.9
  Compute TSPs  :  13.82
  Visualisation  :  0.3
In [78]:
heuristic2.plot_steps()
In [79]:
heuristic2.solution_best
Out[79]:
Solution with a total cost of 50.19  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  3.6644

Without time splitting

In [80]:
problem3 = problem.copy()
problem3.H = 2
problem3
Out[80]:
Parameters of the problem : 
         Number of time steps : 4 
         Number of schools : 107 
         Number of warehouses : 1 
          Name of the warehouses : ['BUJUMBURA'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 10 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 4 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 2 
         Number of virtual time steps between segments : 0.5 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0.5
In [81]:
param
Out[81]:
 Meta parameters of the heurestics : 
 
 For iterations : 
     Length of segments (delta) : 10 , 
     Tau (the temperature) begins at 3.0, finishes at 0.1 and is cooled by 0.9 --> 32 steps 
  
 Inside algorithm's parameters : 
     Bounds of epsilon  : (0.05, 0.15) , 
     For randomizing G (ksi) : 0.142 
 
     Operators' parameters : 
     Sigmas for updating the weigths of the operators (10, 5, 2), with reaction factor : 0.8 , 
     Percentage rho for operators : 0.3 , 
     Solver used for the MIP : CBC
In [82]:
heuristic3 = Matheuristic(problem3,param)
heuristic3.algo2()

Duration constraint looks infeasible
Duration constraint looks infeasible
Duration constraint looks infeasible
Duration constraint looks infeasible
Duration constraint looks infeasible
Duration constraint looks infeasible
Duration constraint looks infeasible
 Total algorithm time = 1273.26 
Total ISI running times : 
  Define problem  :  540.33
  Solve problem   :  652.49
  Compute TSPs  :  17.83
  Visualisation  :  0.29
In [83]:
heuristic3.plot_steps()
In [84]:
heuristic3.solution_best
Out[84]:
Solution with a total cost of 52.686  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  3.4396

Without virtual time step

In [85]:
problem4 = problem.copy()
problem4.t_virt = 0
problem4.time_fuse(1/problem.t_virt)
problem4
Out[85]:
Parameters of the problem : 
         Number of time steps : 2 
         Number of schools : 107 
         Number of warehouses : 1 
          Name of the warehouses : ['BUJUMBURA'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 10 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 2 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 1 
         Number of virtual time steps between segments : 0 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0
In [86]:
param
Out[86]:
 Meta parameters of the heurestics : 
 
 For iterations : 
     Length of segments (delta) : 10 , 
     Tau (the temperature) begins at 3.0, finishes at 0.1 and is cooled by 0.9 --> 32 steps 
  
 Inside algorithm's parameters : 
     Bounds of epsilon  : (0.05, 0.15) , 
     For randomizing G (ksi) : 0.142 
 
     Operators' parameters : 
     Sigmas for updating the weigths of the operators (10, 5, 2), with reaction factor : 0.8 , 
     Percentage rho for operators : 0.3 , 
     Solver used for the MIP : CBC
In [ ]:
heuristic4 = Matheuristic(problem4,param)
heuristic4.algo2()

This problem was infeasible !

With higher rho

In [89]:
problem5 = problem.copy()
problem5
Out[89]:
Parameters of the problem : 
         Number of time steps : 4 
         Number of schools : 107 
         Number of warehouses : 1 
          Name of the warehouses : ['BUJUMBURA'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 10 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 4 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 2 
         Number of virtual time steps between segments : 0.5 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0.5
In [90]:
param5 = deepcopy(param)
param5.rho_percent = 0.6
In [91]:
heuristic5 = Matheuristic(problem5,param5)
heuristic5.algo2()

Duration constraint looks infeasible
Duration constraint looks infeasible
 Total algorithm time = 1041.59 
Total ISI running times : 
  Define problem  :  409.15
  Solve problem   :  573.16
  Compute TSPs  :  14.44
  Visualisation  :  0.24
In [92]:
heuristic5.plot_steps()
In [93]:
heuristic5.solution_best
Out[93]:
Solution with a total cost of 58.054  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  4.7782

With lower rho

In [94]:
problem6 = problem.copy()
problem6
Out[94]:
Parameters of the problem : 
         Number of time steps : 4 
         Number of schools : 107 
         Number of warehouses : 1 
          Name of the warehouses : ['BUJUMBURA'] 
   Parameters specific to transportation : 
         Number of vehicles in total : 10 
         Cost per kilometers done : 10.0 
         Capacity of trucks for pickups : 20 
         Capacity of trucks are from  : 18.0  to 20  
   Parameters specific to time steps : 
         Number of time steps : 4 
         Length of a time step (in weeks) : 0.5 
         Length of time horizon segment for optimization (H) : 2 
         Number of virtual time steps between segments : 0.5 
  Duration constraint : 
         Maximum time spending in a tour : 10 
         Loading time at each school : 0.5 
         Speed of vehicules : 40 
         Number of virtual time steps between segments : 0.5
In [95]:
param6 = deepcopy(param)
param6.rho_percent = 0.1
In [96]:
heuristic6 = Matheuristic(problem6,param6)
heuristic6.algo2()

 Total algorithm time = 1145.59 
Total ISI running times : 
  Define problem  :  449.03
  Solve problem   :  631.71
  Compute TSPs  :  13.98
  Visualisation  :  0.25
In [97]:
heuristic6.plot_steps()
In [98]:
heuristic6.solution_best
Out[98]:
Solution with a total cost of 65.61  
 Constraints fulfilled : 
  Truck constraint  :  True
  Duration constraint  :  True
  I_s constraint  :  True
  I_w constraint  :  True
  
 Running time : 
  visualisation  :  4.1924
In [ ]: